Question

If $p_1$ and $p_2$ are two odd prime numbers such that $p_1>p_2$, then $p_1^2-p_2^2$

• A. An even number
• B. An odd prime number
• C. An odd number
• D. A prime number

Answer 1

The correct option is A An even number

Let the two odd prime numbers $p_1$ and $p_2$ be $7$ and $5$ respectively.

Then, $p_1^2=7^2=49$

and, $p_2^2=5^2=25$

So, $p_1^2-p_1^2=49-25=24$ which is an even number.

Take another examples with $p_1$ and $p_2$ be $17$ and $13$.

Then, $p_1^2={17}^2=289$

and, $p_2^2={13}^2=169$

So, $p_1^2-p_1^2=289-169=120$ which is an even number.

In general the square of odd prime number is odd.

Hence, the difference of square of two prime numbers is even.

So, $\text{A}$ is the correct option.